Q: What are the factor combinations of the number 13,731,965?

 A:
Positive:   1 x 137319655 x 274639313 x 105630519 x 72273565 x 21126195 x 144547247 x 555951235 x 11119
Negative: -1 x -13731965-5 x -2746393-13 x -1056305-19 x -722735-65 x -211261-95 x -144547-247 x -55595-1235 x -11119


How do I find the factor combinations of the number 13,731,965?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 13,731,965, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 13,731,965
-1 -13,731,965

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 13,731,965.

Example:
1 x 13,731,965 = 13,731,965
and
-1 x -13,731,965 = 13,731,965
Notice both answers equal 13,731,965

With that explanation out of the way, let's continue. Next, we take the number 13,731,965 and divide it by 2:

13,731,965 ÷ 2 = 6,865,982.5

If the quotient is a whole number, then 2 and 6,865,982.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 13,731,965
-1 -13,731,965

Now, we try dividing 13,731,965 by 3:

13,731,965 ÷ 3 = 4,577,321.6667

If the quotient is a whole number, then 3 and 4,577,321.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 13,731,965
-1 -13,731,965

Let's try dividing by 4:

13,731,965 ÷ 4 = 3,432,991.25

If the quotient is a whole number, then 4 and 3,432,991.25 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 13,731,965
-1 13,731,965
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

15131965952471,23511,11955,595144,547211,261722,7351,056,3052,746,39313,731,965
-1-5-13-19-65-95-247-1,235-11,119-55,595-144,547-211,261-722,735-1,056,305-2,746,393-13,731,965

More Examples

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